Alcohol is easier to obtain, and cheaper on trail, though you might have to buy more than you need (12 oz HEET is a reasonable quantity, but still 12 oz). I like alcohol for weekend trips.
Esbit has more BTU's/oz. I find that a half tab will heat up, but not boil, two cups of water, while a full tab will bring 3 cups of water to a boil in most conditions. I can get by with two tabs (one ounce) of Esbit a day to heat up 4 cups of water for dinner and two for breakfast.
I would have to carry 1.5 oz/day of alcohol to do the same thing.
So, I like Esbit for extended trips where I will be carrying 4-10 days of food, as it minimizes my fuel weight.
For a 3-week AT section hike, I mailed myself Esbit in resupply boxes so that I did not have to worry about finding or buying fuel on trail. This worked well for me, but means I can't tell you how easy it would have been to find it. One box is 12 tabs, which would be enough for 6 days of use for me.